Amazon Inc.’s agreement to buy an online pharmacy sets the stage for the internet retailer to make it more convenient to fill a prescription. But the deal alone won’t likely address a bigger problem for patients and their employers: the high cost of many drugs.

The purchase of PillPack will give Amazon a platform to sell medicines but not alter how high-priced drugs are paid for, industry experts say. And the deal doesn’t yet give Amazon the expertise to handle the costliest drugs—biotech medicines that require special handling.